A211416 Number of self-inverse 2 X 2 matrices with all terms in {-n,...,0,...,n}.

0, 14, 22, 38, 54, 70, 86, 102, 134, 150, 166, 182, 214, 230, 246, 278, 310, 326, 342, 358, 390, 422, 438, 454, 518, 534, 550, 566, 598, 614, 646, 662, 694, 726, 742, 774, 806, 822, 838, 870, 934, 950, 982, 998, 1030, 1062, 1078, 1094, 1158, 1174

Offset

0,2

Links

Table of n, a(n) for n=0..49.

Example

The 14 matrices counted by a(1) are as follows:
  ...
1 0...-1 0...-1 -1...-1 0...-1 0...-1 0...-1 1
0 1... 0 -1...0  1...-1 1....0 1 ...1 1... 0 1
  ...
0 -1...0 1...1 -1... 1 0....1 0....1 0....1 1
-1 0...1 0...0 -1...-1 -1...0 -1...1 -1...0 1

Mathematica

t[n_] := t[n] = Flatten[Table[w^2 + x*y - 1, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 20}]  (* A211415 *)
t + 2                        (* A211416 *)
(t + 2)/2    (* integers *)
t/4          (* integers *)
(t/4 - 1)/4  (* integers for n>1 *)

Crossrefs

Cf. A211415.

Sequence in context: A183185 A324526 A259750 * A045282 A039291 A043114

Adjacent sequences: A211413 A211414 A211415 * A211417 A211418 A211419

Keyword

nonn

Author

Clark Kimberling, Apr 09 2012

Extensions

Offset corrected by Pontus von Brömssen, Jan 22 2020

Status

approved